Method of iterative compensation for non-linear effects in three-dimensional exposure of resist

ABSTRACT

The field of this disclosure is making three-dimensional topographic structures by means of graduated exposure in a photosensitive material, such as a photoresist, photosensitive polymide, or similar. Such patterns may be written either to be used directly as optical, mechanical, fluidic, etc. components, e.g. diffusors, non-reflecting surfaces, Fresnel lenses and Fresnel prisms, computer-generated holograms, lenslet arrays, etc, or to be used as masters for the fabrication of such components by replication. Replication can be done by molding, pressing, embossing, electroplating, etching, as known in the art. This disclosure includes descriptions of using passive absorbing components in thin resist, using high gamma thick resists with high resolution pattern generators, using multiple focal planes including at least one focal plane in the bottom half of the resist, and iterative simulation of patterning and adjustment of an exposure map.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 61/107,581, entitled, “Method of Iterative Compensationfor Non-Linear Effects in Three-Dimensional Exposure of Resist,” filedon 22 Oct. 2008.

This application further claims the benefit of U.S. ProvisionalApplication No. 61/107,588, entitled “Method of Compensation forBleaching of Resist During Three-Dimensional Exposure of Resist,” filedon 22 Oct. 2008.

The application further claims the benefit of U.S. ProvisionalApplication No. 61/107,591, entitled “Multi-Focus Method of EnhancedThree-Dimensional Exposure of Resist,” filed on 22 Oct. 2008. All theseprovisional applications are hereby incorporated by reference for allpurposes.

This is one of three applications filed contemporaneously. The three areentitled, “Method of Iterative Compensation for Non-Linear Effects inThree-Dimensional Exposure of Resist,” application Ser. No. ______;“Method of Compensation for Bleaching of Resist During Three-DimensionalExposure of Resist,” application Ser. No. ______; and “Multi-FocusMethod of Enhanced Three-Dimensional Exposure of Resist,” applicationSer. No. ______.

Three PCT applications of the same titles also have been filed inEnglish and designating the United States on Oct. 21, 2009 by applicantMicronic Laser Systems. The contemporaneously filed US applications andrecently filed PCT applications are hereby incorporated by reference forall purposes.

BACKGROUND OF THE INVENTION

The field of this disclosure is making three-dimensional topographicstructures by means of graduated exposure in a positive-tonephotosensitive material, such as a photoresist, photosensitive polymide,or similar. Typically the produced surfaces have a surface profile whichis non-reentrant, i.e. for each lateral point (x, y) the surface hasonly one height z(x,y) or there may be points where the surface isapproximately vertical (perpendicular to the xy plane). Alternativelythey may be said to have only positive slopes (including approximately90 degrees to the xy plane, but no significantly negative (overhanging)slopes. The surfaces may be called 2.5D surfaces since they have moredimensions than the xy plane, but are significantly more constrainedthan a 3D surface. Many relevant surfaces will have only positiveslopes.

Such 2.5D patterns may be written in positive resist either to be useddirectly as optical, mechanical, fluidic, etc. components, e.g.diffusors, non-reflecting surfaces, Fresnel lenses and Fresnel prisms,computer-generated holograms, lenslet arrays, etc, or to be used asmasters for the fabrication of such components by replication.Replication can be done by molding, pressing, embossing, electroplating,etching, as known in the art.

Useful and compact introductions to resist exposure and development canbe found at http://www.microchemicals.eu/technical-information,especially the articles entitled “Exposure of Photo Resists,” 5 pp.revised 2007 Mar. 12; “Optical Parameters of Photoresists,” 2 pp.,revised 2007 Feb. 26; and “Development of Photoresists,” 3 pp., revised2007 Feb. 28.

FIG. 1 shows a process for creating a 2.5D surface structure on aworkpiece by means of varying exposure of a photoresist as known in theart. In FIG. 1 a, a positive-tone photoresist 101 is applied to aworkpiece 102. In FIG. 1 b, the resist is exposed to electromagneticradiation 103 with higher 104 and lower 105 exposure dose in an exposuresystem 106. In FIG. 1 c, the developer 107 dissolves part of the resist.Areas exposed to a higher dose 104 dissolve faster than areas exposedwith less dose 105, creating a three-dimensional surface pattern 108, asdepicted in FIG. 1 d. The profile can be used directly (as shown inFIG., scattering light in a controlled fashion.) It can be transferredinto a material with more durable or otherwise more suitable properties109, as in FIG. 1 f. It can be used for replication of thethree-dimensional pattern 110, as shown in FIG. 1 g.

Positive tone in this disclosure means that the developer removes resistthat is exposed above a certain dose, the threshold. Resists with highcontrast (high gamma) have a sharp on-set of dissolution at thethreshold dose, while for resist with low contrast (low gamma) thedissolution rate is more proportional to the dose. This is illustratedin the article, “Exposure of Photo Resists,” supra, available athttp://www.microchemicals.eu/technical-information. The article positsthat grey scale lithography uses low contrast resist, rather than highcontrast resist.

Negative-tone resists, e.g., SU-8, become insoluble with increasingexposure dose. Since there is always some absorption in the resist thedose is higher at the top surface than close to the substrate, and it isonly when the resist is fully exposed that it will adhere to thesubstrate after development. Partially exposed features or areas willfall off or peel during development or rinsing. Therefore negative-toneresists tend to be less suitable to the writing of 2.5D surfaces.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a process to make a three-dimensional pattern in a positiveresist as known in the art. In FIG. 1 a, a photoresist 101 is applied toa workpiece 102.

The resist is exposed to electromagnetic radiation 103 with higher 104and lower 105 exposure dose in an exposure system 106, FIG. 1 b.

In FIG. 1 c, the developer 107 dissolves part of the resist.

Areas exposed to a higher dose 104 dissolve faster than areas exposedwith less dose 105, creating a three-dimensional surface pattern 108,FIG. 1 d.

The profile can be used directly (here shown to scatter light in acontrolled fashion, FIG. 1 e), transferred into a material with moredurable or otherwise more suitable properties 109, FIG. 1 f, and/or usedfor replication of the three-dimensional pattern 110 as shown in FIG. 1g.

FIG. 2 a shows a diagram of the dissolution rate versus dose for twodifferent resist-developer systems.

FIG. 2 b shows a diagram of the remaining resist thickness afterdevelopment of the two resist systems in FIG. 2 a.

FIG. 2 c shows the dose sensitivity of the resists in FIG. 2 a.

FIG. 3 a shows a diagram of the remaining resist thickness afterdevelopment of a resist dominated by bleaching.

FIG. 3 b shows the dose sensitivity of the resists in FIG. 3 a.

FIG. 4 a shows a diagram of the remaining resist thickness afterdevelopment of a resist dominated by absorption.

FIG. 4 b shows the dose sensitivity of the resists in FIG. 4 a.

FIG. 5 depicts a simulated semi-sphere, after development, written usinga laser scanning system and 20 μm thick resist.

FIG. 6 depicts improved faithfulness of the latent image to the ideal,after 5 iterations of simulation and exposure adjustment.

FIGS. 7-8 depict uncorrected and corrected exposure to produce a latentimage with one box set on top of another. FIG. 7 shows the result ofapplying an exposure that matches desired result.

FIG. 8 depicts the improved exposure pattern and result after 10iterations of modeling and exposure pattern adjustment.

FIGS. 9-10 depict uncorrected and corrected exposure to produce a latentimage of three rounded features in a row. FIG. 9 shows the result ofapplying an exposure that matches desired result.

FIG. 10 depicts the improved exposure pattern and resulting latent imageafter 10 iterations of modeling and exposure pattern adjustment.

FIG. 11 illustrates use of a reduced etch rate to improve featurecritical dimension (CD) accuracy.

FIG. 12 illustrates collecting data regarding the effect of etch rate asfunction of feature CD.

FIG. 13 illustrates compensation based on the data collectionillustrated by FIG. 12 and result of this compensation.

FIG. 14 illustrates M=3 different planes.

FIG. 15 adds to FIG. 14 a representation of varying pixel sized indifferent exposure phases.

FIGS. 16 and 17A depict beam divergence patterns in resist layers thatare 1 and 80 μm thick, respectively. FIG. 17B is an enlargement of asection of the 80 μm thick resist divergence pattern, that shows asection 5 μm thick, from the center of the thicker layer.

FIG. 18 shows the difference between ideal and exposed in a 20 μm resistlayer, when the focal plane is set at 10 μm.

FIG. 19 applies a focal plane selection algorithm to the semi-spherepattern, depicting gradients and the gradient distribution.

FIG. 20 selection of a focal plane.

FIG. 21 a feature with multiple vertical corners, for which multiplefocal planes are preferred.

FIGS. 22-23 are photo micrographs of resist features actually produced,with better and worse focal plane positions.

FIG. 24 illustrates alternative partitions between focal planes, incases of one and two writing passes.

FIG. 25 shows a flow chart of a focal plane algorithm.

FIG. 26 depicts a method and device for writing thin resist.

FIG. 27 extends the method and device of FIG. 26 to thick resist.

FIG. 28 depicts writing to multiple focal planes, which could be ineither thin or thick resist.

FIG. 29 depicts iterative refinement of an exposure map.

DETAILED DESCRIPTION

The following detailed description is made with reference to thefigures. Preferred embodiments are described to illustrate the presentinvention, not to limit its scope, which is defined by the claims. Thoseof ordinary skill in the art will recognize a variety of equivalentvariations on the description that follows.

Creating a three-dimensional profile in a resist is a non-linearprocess, which means that the depth of resist removed by development isnot linearly proportional to the exposure dose. Instead, the inputpattern may be specified as a depth after development and a method maybe applied to translate the specified depth into an exposure dose, e.g.by using a calibrated look-up table or mathematic expression. Theexposure dose creates a latent image that is developed in an effort togive the desired depth profile.

A small variation in amounts of exposure dose gives a relatively smallchange in dissolution rate during development, but not a linearlyproportional change. In prior processes, it is difficult to control thedepth with an accuracy of +/−1%, which may be required for opticalsurfaces. The depth after development will be affected by smalldisturbances, such as the baking temperature of the resist, fluctuationsof the laser power, thickness variations of the resist, agitation of thedeveloper, etc. The dose errors are often lumped together withsensitivity fluctuations and developer activity variations. The combinedequivalent dose error is typically within the range of 1-5%. The priorprocess is based on close control of the dissolution rate in thedeveloper by the exposure dose is difficult to keep stable and oftenneeds frequent recalibrations. Even with recalibration, a process thatdepends on a closely controlled dissolution rate and time withoutautomatically compensating for non-linear effects, such as bleachingeffects, will not consistently produce results within +/−1% of the idealfeature.

The problem with the prior process depicted in FIG. 1 is its sensitivityto disturbances. Slight variations in the dose, such as variations dueto laser noise, and variations in the resist properties or the developeragitation, cause depth variations in the finished profile. Likewise, thetime and temperature control during development is critical.

An opportunity arises to introduce new processes for controlling thedepth and shape of features exposed in a relatively thick resist layer,preferably with an accuracy of +/−1%. Better, more easily controlled2.5D feature formation may result.

The relationship between exposure dose and relief height is complex andinvolves non-linear effects. The problem underlying the herewithpresented invention is to be seen in providing a method of forming athree-dimensional latent image with good depth and shape control in alayer of resist. By iteration, the present invention automaticallyimproves on and refines the exposure dose for a particular relief map.In addition, the method disclosed herein automatically takes intoaccount non-linear effects in the resist. Two or more iterations may beused for producing the exposure map with point-to-point exposure dosecalculated to exceed an exposure threshold of the resist at a pluralityof controlled depths within the resist layer. By simulating thepatterning of the resist layer and comparing the simulatedthree-dimensional latent image to the relief map, the dose levels of theexposure map are adjusted as a result of the comparing step.

According to certain embodiments of the present invention,pre-determined rules or a model of the exposure and development processmay be used to compensate for non-linear effects. The rule-based, ormodel-based, compensation may automatically adjust the gray-scalevalues, e.g. the gray-scale values of the modulator pixels of thepattern generator, as a function of feature precision requirements,feature area and/or the gradient field. The height information for theexposure pattern may be adjusted by the rules or the model, eithermathematically or in grey scale, e.g. by automatically adjusting themodulator gray-scale values of the pattern generator used for exposingthe resist. In order to speed up the iterative method proposed above, arule-based model may be used to give a first exposure map converted fromthe relief map and with initial exposure dose levels as the initialinput to the iterative loop of simulating the exposure map by repeatedlycomparing the simulated exposure map to the relief map.

The etch rate (or dissolution rate) selected, e.g. in a DRIE process,may give different z-depths for patterns with different featureprecision requirements, feature areas and/or gradient fields, even ifthe patterns have the same z-depth in the relief map, e.g. a CADpattern, representing the three-dimensional surface. The above-mentionedrule-based, or model-based, compensation may also compensate for theetch rate, or dissolution rate, selected.

When translating relief depths to exposure doses in a scanning system,the asymmetry related to the sweep direction of a scanning writing laserbeam exposing the resist may be taken into account and be compensatedfor, e.g. including sensitivity of exposure to whether the exposingenergy is waxing or waning. In a raster-scan pattern generator, there isa difference between a first feature edge (change from no dose to highdose), and the second edge (change from high dose to no dose.) In thedirection of scanning, and since the exposing beam spot has a finitewidth, the first encountered edge will receive a lower dose than thesecond edge. The second edge will absorb slightly less dose than thefirst edge, since it has already been partly bleached by the lightexposing the previous position or pixel. This will create an effectivetilt in the exposure. Whether it is a first or a second feature edgethat is exposed may also be automatically compensated for according tocertain embodiments of the present invention. Other issues that may beusefully addressed by introducing pre-determined rules and/or acompensation model when translating relief depths to exposure dosesinclude absorption of exposure doses, and photonic and chemical/physicalprocesses in exposure and development.

Background on 2.5D Exposure

We disclose methods to generate three-dimensional microstructures, ornanostructures, using direct laser writing in a thick photoresist layer.Many of these surfaces are 2.5D or non-reentrant surfaces as definedabove. One way previously described to manufacture such structures is touse a pre-fabricated photo-mask having a grey scale pattern, and exposethe photoresist through that mask for a sufficient time to reach asufficient exposure dose [mJ/cm2]. In direct writing using an opticalpattern generator, on the other hand, the exposing dose may be alimiting factor. By superposition of N separate exposure passes,sufficient dose can be applied to create the desired latent image in theresist.

The N-pass writing is further utilized as a means for averaging outseveral different possible pattern-deteriorating effects labeled by theJapanese word Mura. Improved performance in all three dimensions (x, y,z) can be achieved by shifting the writing grid an appropriate distancein both the x- and y-directions. The exposure doses are set from resistdepth-vs-dose characteristics, which take into consideration thenon-linear depth-to-dose relationship, and absorption, bleaching anddefocus properties in the photoresist.

Writing Systems

The writing system used is a direct-writing pattern generator, incontrast to systems that use masks as an intermediate step. Thedirect-writing system converts an input description of the 2.5D pattern,e.g., a list of (x, y, z) coordinates, to a bitmap and writes thebitmap, suitably converted to expose the resist. The writing system hasa stage for holding the workpiece, a source of electromagnetic radiationin the range of 460 nm or less, e.g., a laser at approximately 413, 364,355, or 266 nm wavelength. It includes focusing optics and a modulatorfor the radiation. Several architectures are possible: scanning one orseveral beams with an acoustooptic or mechanical scanner, scanning thestage under an array of projected light spots, scanning the stage inrelation the image of a spatial light modulator, either projecting a 1Dline or 2D area of contiguous modulated pixels, or an array of lightspots individually modulated. What is more important than the actualmode of scanning or creation of the image is to have a high dynamicrange and, preferably, a high maximum dose.

Suitable modulators include acoustooptic and electrooptic modulators anddirectly modulated lasers. micromechanical Spatial Light Modulators(SLMs) such as Grating Light Valves (GLVs from Silicon Light Machines)and Digital Mirror Devices (DMDs from Texas Instruments) as well asanalog SLMs (from Micronic Laser Systems and Lucent) also may besuitable. Analog SLMs may rely on either tilting or piston drivenmirrors. Either configuration may render shades of grey due todestructive interference effects.

Multi-Pass Writing

Binary modulators such as the DMD may achieve high-dynamic rangegrey-scale modulation first by having 10,000:1 or better contrast, andsecondly by writing many passes with different doses, e.g., with dosescorresponding to powers of two. A pattern of 12-bit grey values may bewritten in 12 binary passes. It may be beneficial to use even morepasses, such that the binary passes with highest dose are subdividedinto multiple passes which build up the high dose gradually. If thetotal dose is higher than approximately two times the maximum dose thatcan be delivered in a pass several passes at high dose can be used toaccumulate the needed dose. Additional passes with less dosage may beused in a hybrid multi-pass scheme to get any dose value less than themaximum dose. For example, a six-bit grey value in the range 0-127 unitsmight in this way be written in a writer capable of delivering maximum16 units per pass, by combining in a hybrid multi-pass scheme a numberof high-dose passes (here 7 passes) with a number of passes with lowerdose (4 passes). Any dose in the range 1-127 units can thus be writtenin 11 binary passes with the doses 1+2+4+8+16+(16+16)+(16+16+16+16).This allows higher doses to be deposited in the resist than either theresist or the writing system is capable of in a single pass.Alternatively, binary writing passes may gain grey scale precision byusing passes with less than a factor of two in difference, such as afactor of the square root of three: 1.0, 1.7, 3.0, 5.4, 9.0 units. Asequence with less than a factor of two grey scale differences may havemore than one possible representation for a grey value; it is possibleto choose the one which adds up closest to the actual grey value. In thesequence above, with a step of sqrt(3), the value 10 can beapproximately represented as 1.0+9.0 or 1.7+3.0+5.4. During calibration,the dose sum that best represents the value 10, for instance, using theactual values in the multipass scheme can be chosen. The passes withless than a factor of two difference may be combined into a hybridmulti-pass scheme. For instance, passes of 1.0, 1.7, 3.0, 5.4 dose unitsplus ten passes with a 9.0 dose can span a range of 1-100 dose units,using a writer that delivers up to 9 dose units in a single pass.

Overview of Iterative Exposure Calculation, Absorption and MultipleFocal Planes

Exposure with scanning laser light may be modeled as Gaussian beams witha Gaussian intensity distribution. Other optical power densitydistributions are naturally possible. The beam, or beams in a multi-beamwriter, can be focused in the laser writer tool's final lens systemeither on the upper surface of the photoresist, or somewhere between theresist surface and the substrate surface in the downwards z-direction.During propagation through the photoresist layer, a Gaussian beamdiverges (widens) due to its wave property, making the resulting lateral(x, y) as well as vertical (z) writing resolution deteriorate. Thedepth-of-focus is determined by the numerical aperture (NA) of the lenssystem of the writer system, together with the refractive index of thephotoresist and of the ambient medium. Furthermore, the power density ordeposited/absorbed exposure dose varies with the depth in the resist.

In generation of some 2.5D structures by direct-write (laser)lithography, the resist may be much thicker than in ordinary 2Dmicrolithography, such as lithography to produce semiconductor circuitsand LCD or OLED displays. When the photoresist is thicker than thedepth-of-focus of the writer tool, the spot size varies by depth(z-level) in the photoresist.

The iterative modeling and dose selection part of this disclosurediscloses methods of compensating for linear and non-linear response toexposing radiation of a relatively thick resist layer. When 2.5Dpatterning of thick resist is addressed, nonlinear effects becomeimportant.

Bleaching is one of the nonlinear effects. By bleaching, we mean achange in the optical absorption of a resist as it is exposed toradiation. This bleaching may result from absorption of energy and mayalso depend on the time between exposure passes or other phenomena.

A second kind of optical absorption does not expose the resist; itconverts photons to heat. Dyes, pigments or nano-particles in resisthave this effect, as well as some of the chemical agents making up theresist. With non-bleachable absorption, the exposure dose requiredbecomes exponential with depth.

Multi-focal plane exposure is a method of compensating for the thicknessof a thick resist layer and/or improving the fidelity ofthree-dimensional patterning. Multi-focus involves focusing at variousdepths in the resist, such as at the top, in the middle, and near thebottom, and assigning varying amounts of exposure dose to each of thefocal planes. For modestly thick resist layers, a single focal plane maybe sufficient, positioned between the top and bottom of the resistlayer. Often, a single focal plane in the bottom half of the resist,away from the exposed surface, will produce favorable results forreasons explained below.

The iterative modeling approach can readily take into account bleaching,dye and/or multi-focus exposure. Bleaching and dye can be taken intoaccount when choosing how to apply multi-focus exposure, particularly asthe top portion of the resist bleaches.

Iterative Analysis and Exposure after Modeling

Issues that can usefully be addressed when translating relief depths toexposure doses include asymmetrical response to the sweep direction ofscanning writing laser beams, absorption of exposure doses, and photonicand chemical/physical processes in exposure and development.

One of the problems in 2.5D microlithography is asymmetry related to thescan direction of an exposing laser beam, i.e. sensitivity of exposureto whether the exposing energy is waxing or waning. In a raster-scanpattern generator, there is a difference between a first feature edge(change from no dose to high dose), and the second edge (change fromhigh dose to no dose.) In the direction of scanning, and since theexposing beam spot has a finite width, the first encountered edge willreceive a lower dose than the second edge. The second edge will absorbslightly less dose than the first edge, since it has already been partlybleached by the light exposing the previous position or pixel. This willcreate an effective tilt in the exposure. FIG. 5 depicts a simulatedsemi-sphere, after development, written using a laser scanning systemand 20 μm thick resist. The scan is proceeding from left to right, sothat left hand side of the semi-sphere is exposed first. The resistmodel used to simulate the dynamic system takes into account bleachingof the resist. The semi-sphere is the ideal, desired shape of the resistafter development and, therefore, the desired shape of the latent imageafter exposure and before development. As the simulation shows, apattern of exposing radiation that matches the ideal pattern produces alatent image that is skewed to the left. This is readily apparent in thedifference graph in the middle of FIG. 5, which shows that thedifference is asymmetrical between the left and right edges of thefeature.

A dynamic model of 2.5D latent image formation can take into account atleast three exposure-energy-absorbing processes. First, α_(Exp)non-bleaching absorption leading to developable exposures, ordinarilycreated by the concentration of the Photo-Active Compound (PAC). Second,α_(Exp, Bleach) leading to developable exposures with a component thatis so-called bleachable, that has an absorption that diminishes withincreasing absorbed exposure dose. This can be mathematically expressedas a linear approximation using two derivatives:

$\frac{\partial\alpha_{Exp}}{\partial z}\mspace{14mu} {or}\mspace{14mu} \frac{\partial\alpha_{Exp}}{\partial D}$

where D is the exposure dose. Thus, one may express the change of thebleachable absorption as:

${\alpha_{Exp}(z)} \approx {{\alpha_{0}\left( {z = 0} \right)} + {d \cdot \frac{\partial\alpha_{Exp}}{\partial z}}}$${\alpha_{Exp}(D)} \approx {{\alpha_{0}\left( {D = 0} \right)} + {d \cdot \frac{\partial\alpha_{Exp}}{\partial D}}}$

A third energy absorption component, represented by α_(Dye) convertsabsorbed photon energy to heat, rather than resist development. A dye oranother photon absorbing substance in the resist has this effect.

The response to the exposing light/radiation in the photoresist may beseparated generally into photonic and chemical/physical effects. Thephotonic effects, include an inherent proximity effect caused by theconvergence and divergence of the focused light in the photoresist,light scattering in the optical system, light scattering in thephotoresist, reflections at the substrate etc. The chemical/physicaleffects include the influence from the soft-bake of the resist, thedehydration and rehydration of the resist, the photo-chemical reactionsduring the exposure, the physical-chemical diffusion processes duringand after the exposure, and the concentration-, temperature- andagitation-influences during the development.

Examples of Iterative Adjustment of Exposure

FIG. 6 depicts improved faithfulness of the latent image to the ideal,after 5 iterations of simulation and exposure adjustment. The ideal andexposed patterns are virtually indistinguishable in the top part of thefigure, which is significant improvement over the results depicted inFIG. 5. The scale of the difference graph in FIG. 6 is adjusted from thescale in FIG. 5, because the difference is small. As the bottom part ofFIG. 6 shows, the exposure pattern is not a semi-sphere afteradjustment, but the exposed result in a latent image or afterdevelopment closely approximates the ideal.

FIGS. 7-8 depict uncorrected and corrected exposure to produce a latentimage with one box set on top of another. FIG. 7 shows the result ofapplying an exposure that matches desired result. The exposing radiationprofile is shown at the bottom. The exposed result is compared to theideal at the top. The middle part of FIG. 7 shows the difference in theexposed pattern, between ideal and actual.

FIG. 8 depicts the improved exposure pattern and result after 10iterations of modeling and exposure pattern adjustment. The proximityeffects related to exposing a thick photo resist with a complex patternare corrected by iterative modeling and exposure adjustment.

FIGS. 9-10 depict uncorrected and corrected exposure to produce a latentimage of three rounded features in a row. FIG. 9 shows the result ofapplying an exposure that matches desired result. The exposing radiationprofile is shown at the bottom. The exposed result is compared to theideal at the top. The middle part of FIG. 9 shows the difference in theexposed pattern, between ideal and actual.

FIG. 10 depicts the improved exposure pattern and resulting latent imageafter 10 iterations of modeling and exposure pattern adjustment. In thetop image of FIG. 10, the ideal and exposed patters are virtually theproximity effects related to exposing of a thick photo resist with acomplex pattern corrected by iterative modeling and exposure adjustment.

In some circumstances, the exposure pattern is tentatively correctedbefore the latent image is simulated. The algorithm provides rulesand/or a model of the exposure/development process. The result of thistentatively corrected pattern is simulated and fed into an iterativecorrection process. The iterative process can be repeated until theresidual improvement is below a pre-determined threshold.

The aforementioned algorithm is used to compensate for non-linear photoresist processes such as bleaching. Accordingly, the algorithm removesthe extra proximity effects that occur for thick resist and a highoptical NA.

In other circumstances, the algorithm calculates the non-linear effectin some directions in the XY plane and then calculates the totalcorrection as a linear combination of the result. The algorithm maycalculate the non-linear effect in one or a few directions in the XYplane only and then calculate the total correction as a linearcombination of the result.

Impact of Etch Rate and Minimum Line Width Requirements

FIG. 11 illustrates use of a reduced etch rate to improve so-calledfeature size, lateral dimension, or line width variation, which is alsosometimes referred to by the shorthand “CD” variation, for featurecritical dimension variation or accuracy. Changes in etch rate impactthe minimum line widths typically achieved. This is interrelated to thefeature area and gradient field in a pattern. The etch rate for a deepreactive ion etch (DRIE) process is often treated as dependent on theminimum line widths or feature sizes and the gradient field in the areaetched. The dissolution or removal rate for some thick photoresists is afunction of the minimum line widths or feature sizes and the gradientfield, as shown in FIG. 6. Depending on the etch rate selected, theetching in a DRIE process applied to thick photoresists will givedifferent z-depths for patterns with different feature precisionrequirements, feature areas and gradient fields, even if the patternshave the same z-depth in the CAD-pattern.

FIG. 12 illustrates collecting data regarding the effect of etch rate asfunction of feature CD. The relationship between the etch rate (ordissolution rate) and the feature precision requirement, feature areaand gradient field is first identified, before compensation is applied.From this data, a rule-based (or model-based) compensation model iscreated that adjusts the grey-scale as a function of feature precisionrequirement, feature area and gradient field. The feature precisionrequirement and/or similar measurements such as the feature area and/orgradient field are then calculated. Thus, from the function identifiedabove, changes are made in height information for the pattern. This maybe done either mathematically or in grey scale. After the adjustment ismade, each pattern will get the correct depth independently of thefeature CD. Finally, the modified pattern is written.

The proximity effect is caused by the convergence and divergence of thefocused light. By exposing areas that are large compared to theproximity effect, and by measuring the depths in the central regions ofsuch exposed areas for a certain combination of spot size and grid size,the proximity effect influence is measured and can be compensated. Theresulting depth-vs-dose characteristics for the photoresist are thenmore or less dominated by the photo-chemical effects. The proximityeffect-related processes are handled by proximity effect correction andcompensation methods.

FIG. 13 illustrates compensation based on the data collectionillustrated by FIG. 12 and result of this compensation. It illustratesadjusting the exposure dose to change the z-dynamics of the exposedpattern. Exposure of a (positive) photoresist may or may not encounter ableachable PAC. In the development of a positive photoresist, each doselevel is dissolved (etched) with a rate that is a function of, andincreases with, the dose. In timed, rate-dependent processes, control ofthe etch depth d=d(D) requires careful control of development timeT_(Dev). Erroneous T_(Dev) results in erroneous relief depth d anderroneous relief swing Δd. The dissolution rates are also affected bythe developer concentration, the developer temperature, the developmentagitation by flushing, stirring etc., which helps maintain freshdeveloper at the resist surface and avoid accumulation of diffusionbarrier of dissolved resist in the developer. Given these factors, it isuseful for control of relief depths to depend primarily on controllingthe exposure dose.

We disclose an alternative for depth control of 2.5D reliefs thatinvolves an end point approach to developing resist. In ahigh-absorption photoresist that is fully developed until the etch rateshave decreased at least close to zero, the depths are relativelyinsensitive to the (i) development time, (ii) developer concentration,(iii) developer temperature, or (iv) development agitation by flushing,stirring, etc. Instead, the depths depend most heavily on the exposuredose and its precision.

Introduction to Bleaching and Multiple Absorption Processes

Iterative compensation can be applied to a variety of process factors,beyond exposure dose.

For some purposes, a resist with high absorption α_(Exp) is useful. Thehigh absorption α_(Exp) resist may be bleachable. For simplicity, theresult of exposure may be described as a “tube” of constant widththrough the resist, with due to the higher absorption fast decaying dosewith depth. FIG. 16 illustrates a “tube” of exposed resist. At a certaindepth, different for different doses, the exposing number [cm⁻³] ofphotons has decreased to a level where the development dissolution rateapproaches zero. Development means that every dose level is dissolvedwith a both in time, and thus for different resulting depths, varyingdissolution rate. In resist thicker than the exposed depth, thedissolution rate decreases with increasing depth and approaches zero.Full development involves development time that allows the dissolutionrate to go close to zero for the deepest relief levels, where thehighest exposure dose was applied to decrease the greatest featuredepth. With extended development, the control of the final resist depthsfor different doses is governed and controlled by the exposure dose (dueto the high absorption) and not the development time. The exact exposuredose is controlled in the exposure tool.

In other circumstances, a resist with at least two absorption processesis used. The first absorption process described by the coefficientα_(Exp) or α_(Exp, Bleach) results exposure of the resist and formationof the latent image, with bleaching of a first absorbing component. Thesecond absorption process, α_(Dye), increases absorption, but does notcontribute to the exposure of the resist. That can be achieved usingdyed or colored or pigmented resist additives.

The control of the final resist depths for different doses can begoverned and controlled by the exposure dose due to the high absorption,with reduced sensitivity to development time and conditions. Anadvantage of using the exposure dose is that the photon absorption anddepletion is not controlled by the same absorption process responsiblefor the exposure, a process which is also bleachable.

The second absorption process α_(Dye) must be balanced against theavailable photon flux, i.e. the maximum available exposure dose, theexposure absorptions α_(Exp) or α_(Exp, Bleach), the desired maximumrelief depth and the desired relief swing.

If the combined absorption coefficients are too high, then the desiredrelief depth cannot be reached at full development, because theavailable does at depth is too small. If the total absorption resultsare too low then the dissolution rate(s) and the final relief depthswill be controlled by the development time, which is undesired. A usefulcombination of absorption coefficients can be obtained by chemicaltailoring of the various absorption processes to available number ofphotons and the relief to be fabricated.

The various absorption processes can be combined in many ways including:

(i) α_(Exp) or α_(Exp, Bleach) low, and α_(Dye) high.

(ii) α_(Exp) or α_(Exp, Bleach) high, and α_(Dye) low.

Both alternatives may result in a high total absorption. The secondalternative should lead to reduced requirement on available photons,which is useful when available exposure dose is a limiting factor. Theabsorption level becomes high and the dose is limiting when the resistthickness is increased.

Refractive Index and Depth of Focus

Exposure of a thick resist is difficult when the film thickness issubstantially larger than the depth-of-focus of the focus system of theexposure tool. For example, if the laser light is focused at the uppersurface of the photoresist, the laser light or beam will—after thefocus—start to diverge, to widen. Deeper resist regions will be exposedby a wider light beam that shallower regions. Due to Snell's law ofrefraction and the fact that photoresist has a higher refractive indexn_(R) that an ordinary gas ambient such as air or nitrogen, thedepth-of-focus in the resist will be larger than in the atmosphere.Accordingly, it is useful for a resist to have as high n_(R) aspossible. A second target is to adapt the bleaching properties of thephotoresist, which depends on the exposure dose, so that the refractiveindex of the resist does not change too rapidly or too slowly with theabsorbed exposure dose and consequent bleaching. The appropriatecharacteristics of a particular resist can be determined by exposingareas of constant dose, with widths bigger than the proximity effecteffective distance, and by accurately measuring the depths afterdevelopment for the various doses. This yields depth-vs-dosecharacteristics of the resist, which may be expressed as d=d(D). Thecharacteristics may include all non-linear effects as well as bleaching.

Particular Use Cases

By carefully choosing parameters for the exposable absorption processesα_(Exp) and the non-exposable processes α_(Thermal), andα_(Exp, Bleach), the resulting process may be tuned and the performanceof the 2.5D-relief generating tool will be greatly improved.

In some circumstances, the photo-sensitive material is given a highexposure-active absorption via the PAC. The development process may be“terminated” at a certain depth level where all the exposing energy hasbeen depleted. This requires that the amount of exposing energy is not alimiting factor.

According to yet another embodiment, when the amount of exposing energyis not a limiting factor, the photo-sensitive material is exposed to apre-determined absorbed dose. The photo-sensitive material is thendeveloped until the development process ceases at a certain depth in thephoto-sensitive material where there no longer is any exposure energyavailable due to the exposable absorption.

High Gamma Resist with Bleachable and Passive Absorption Components

The technology described in this disclosure provides methods to controla three-dimensional photoresist process better than those known in theart.

FIG. 2 shows the dissolution properties of two fictitious but typicalresists used for microlithography (Resist A) and three-dimensionalprocessing (Resist B). Resist A and its process conditions are chosen togive a high gamma and Resist B a low gamma. Gamma γ is a measure of howfast the dissolution rate changes for a small change of exposure dose,i.e.

γ=(dR/R)/(dE/E)

where R is the dissolution rate as expressed by nm/s and E is theexposure dose as expressed in mJ/cm². Gamma is a unit-less number anddoes not depend on the units chosen to express R and E. There existseveral definitions of gamma, each determined by a different type ofmeasurement. In Mack C., Fundamentals Principles of Optical Lithography,Wiley (2007) the author describes in chapter 7.2 what he calls “measuredcontrast” or γ_(m), determined from the remaining thickness afterdevelopment as a function of dose:

$\begin{matrix}{\gamma_{m} = {{\frac{1}{D} \star \frac{z}{\left( {\ln \; E} \right)}}_{E = E_{0}}}} & \left( {{Mack}\mspace{14mu} 7.21} \right)\end{matrix}$

where D is the full thickness, z the remaining thickness, and E theexposure dose and E₀ the dose where the resist just clears (all resistis removed in the developer). Another measure is the theoreticalcontrast γ_(th), based on dissolution rate instead of thickness:

$\begin{matrix}{\gamma_{th} = \frac{\left( {\ln \; R} \right)}{\left( {\ln \; E} \right)}} & \left( {{Mack}\mspace{14mu} 7.22} \right)\end{matrix}$

where R is the dissolution rate in the developer. We adopt this equationas the gamma definition used in this disclosure, i.e. a resist specifiedto have a gamma of 5 or higher in this disclosure has—in the terminologyof Mack—a theoretical contrast of 5 or higher. It can be determined bymeasuring how deep the developer has dissolved the resist in areas withknown exposure after a fixed period of time. Mack says that if thedevelopment rate varies with the depth into the resist, the measuredcontrast fails to give a good value for the theoretical contrast. Hegives two examples, namely the cases of surface inhibition and ofabsorbing resist. In the case of passively absorbing (non-bleaching)resist Mack gives a relation:

$\begin{matrix}{\gamma_{m} = {\gamma_{th}\left( \frac{1 - ^{{- \alpha}\; {nD}}}{\alpha \; {nD}} \right)}} & \left( {{Mack}\mspace{14mu} 7.29} \right)\end{matrix}$

Mack goes on to propose what he calls “practical contrast” denoted by γwithout any subscript. Practical contrast is based on the how long ittakes for the developer to remove the resist after it has been exposedto varying doses. The theoretical contrast, which is the quantity usedin this disclosure, depends on the detailed chemistry during dissolutionof the resist in the developer.

Photoresists for binary processing, such as those used inmicrolithography, are tuned to have a high gamma, i.e. 5, 8, 12, or even20. These resists do not work well for three-dimensional processing, asshown in FIG. 1. FIG. 2 a shows a diagram of the dissolution rate versusdose for two different resist-developer systems. Resist A in FIG. 2 hasgamma=8, which means that for low doses it has low dissolution rate, andabove a threshold dose the dissolution rate rises very rapidly. If theresist is developed for a predetermined time, the thickness loss will beproportional to the dissolution rate and the time, assuming that thedose is uniform in the vertical direction. Typically, the developmenttimes are fairly long so that the resist has essentially stoppeddissolving any resist at the end of development, sometimes called anendpoint. FIG. 2 b shows a diagram of the remaining resist thicknessafter development of the two resist systems in FIG. 2 a.

The remaining resist thickness in FIG. 2 b is then a steep function ofthe dose. FIG. 2 c shows the change in thickness vs. change in relativedose, i.e. (dD/(D_(max)−D_(min)))/(dE/E), and it is seen that withResist A the remaining thickness, i.e. the profile depth afterdevelopment, is very sensitive to dose and a 3% percent variation indose or sensitivity would give high variation in the thickness, sincethere is an sensitivity that essentially diverges.

When making the three-dimensional patterns, the dissolution typically istimed and not allowed to continue indefinitely. Therefore, the profiledepth is proportional to the development time, i.e.

(dD/D)/(dt/t)=1

where D is the depth and t is the development time. This process iscalled a dissolution-limited process. The process is furthermoresensitive to the temperature, e.g. the activity of the developer maydouble for every 7 degrees and this is magnified by the steepness of thedissolution curve.

When making three-dimensional patterns with Resist A all the depthchange occurs at a very small dose range, e.g. only between 60-80% inthe diagram. With a modulator controlled by a DAC with typically 8 bits,only a small range of the 256 codes would be used to control exposuredose. Obviously, the process described above using a Resist A typeresist as the only resist is not well-suited for creatingthree-dimensional patterns.

Resist B in FIG. 2 is a resist that those of ordinary skill would expectto be used for three-dimensional processing. It has a gamma of 2, whichmeans that the dissolution curve in FIG. 2 a is less steep. Thedevelopment time is also typically less. The remaining resist thicknessis also less steep. The dynamic range is larger, practically 20% to 100%for the maximal dose might be used, since the top surface of the profileis preferably placed some distance from the top of the resist due to thein-homogeneity of the resist close to the surface caused by e.g. drying,chemical segregation, etc. FIG. 2 c shows the dose sensitivity of theresists in FIG. 2 a.

There will be a larger range of dose values used to create the depthrange and a 3% dose variation changes the remaining thickness by at most3% as shown in FIG. 2 c. The sensitivity to relative time changes isequal to Resist A but the sensitivity to temperature is less inflatedthan for Resist A. Overall, Resist B and the process described are moresuitable for creating 2.5D patterns, but still not stable and robustenough to create patterns with depth accuracy requirements of 1% orless. Again, the Resist B process described requires frequentrecalibrations and critical process tuning.

Process Dominated by Bleachable Absorption

FIG. 3 a shows a diagram of the remaining resist thickness afterdevelopment of a resist dominated by bleaching. FIG. 3 a shows a firstprocess in which the remaining thickness for Resist C is dominated bybleaching, which we call a bleaching-limited process. Many commonresists, in particular DNQ-type positive resists, have an absorptionrate of 0.5 per micron or more. When the light exposes the resist, ahydrophobic group is photochemically converted to a hydrophilic acid,allowing the water-based developer access into the resist. Thephotoconverted group has much less absorption after the conversion thanbefore it. The absorption bleaches strongly during exposure and is muchreduced. This is commonly described by so called Dill parameters whichgo into a system of rate equations formulated by Rick Dill at IBM in1975. See, F. H. Dill, et al., “Characterization of positivephotoresist,” IEEE Transactions on Electronic Devices, ED-22, 445-452.Dill parameters, exposure and development of photoresist are discussedin many textbooks on lithography; a recent text is C. Mack, FundamentalPrinciples of Optical Lithography, Wiley, 2007. Optical absorption ofvarious resists is described in the article, “Photoresists OpticalParamaters,” supra, which indicates refractive indexes of 1.65-1.710,depending on wavelength for a number of DNQ resists. Another article onthe same site, “Exposure Phtoresist,” indicates sensitivity of variousresists up to 460 nm.

In a thick resist, which is essentially non-transparent before theexposure, the exposing dose initially reaches only into the first micronor so at the top. After the top layer has been bleached, the lightreaches the layer below it and bleaches it. In this way the light worksits way into the resist. Since the energy to bleach one micron of resistis the same regardless of the position in the resist, the depth to whichthe resist is exposed and bleached is a linear function of the dose. Atdevelopment the resist will develop as far as it is exposed, and theremaining thickness is a linear function of the dose. The thicknesschange vs. the relative dose change has a different curve and isgenerally more benign. As indicated in FIG. 3 a, the dose to bleach theresist is considerably higher than what is needed to expose the resistwithout bleaching. FIG. 3 a shows an example where the resist is exposedfrom top-to-bottom at the dose 1000%, as compared to a 100% dose for anon-bleaching and non-absorbing resist. FIG. 3 shows an idealizedresist, the actual values may differ in an actual process.

The process in FIG. 3 a is suitably applied to a high-gamma resist, suchas Resist A in FIG. 2, with a long development time. The developmentwill then develop through the exposed and bleached part of the resistand stop at a certain dose, which has a very low dissolution rate. Thetiming and activity of the developer will have less influence on theremaining depth and the control of the profiles will be better due tothe more linear depth vs. exposure curve. The result is a process whichis more robust and easier to use in an industrial setting.

Process Dominated by Passive Absorption

FIG. 4 shows a second process with Resist D, which is dominated by anon-bleaching absorption, which we call an absorption-limited process.Like Resist C, Resist D has high gamma and long development, so thedevelopment reaches a point that is little influenced by time andtemperature during development. If the absorption is expressed by α(with the unit per micron), the exposure at the depth D is

E(D)=E ₀exp(−αD)

where E₀ is the exposure at the surface.

The relation can be inverted to give the depth where the exposure is atthe threshold dose E_(th) where with the actual development time thedeveloper effectively stops

D(E _(th))=1/α*ln(E ₀ /E _(th))

or, simplified,

D=c ₁ ln(E)+c ₂

where c₁ and c₂ are constants which implicitly represent α, the resistsensitivity and the development time.

FIG. 4 a shows a diagram of the remaining resist thickness afterdevelopment of a resist dominated by absorption. FIG. 4 b shows the dosesensitivity of the resists in FIG. 4 a.

FIG. 4 b depicts the so-called absorption-limited process. The dosesensitivity is much less than either the dissolution-limited or thebleaching-limited process. The amount by which dose sensitivity issuppressed depends on the relation between the profile depth D_(max) andthe absorption α. The greater the value of α is, the less sensitive theprocess is to relative dose and developer disturbances and the betterthe process control is. However, the exposure dose needed is higher. Asignificantly high value of α will require such strong exposure that theresist may solarise. That is, the resist may reverse its sensitivity andstart getting more difficult to dissolve again, at the top. Likewise, ifthe energy is deposited in a brief time, such as using a laser pulse,the maximum dose may be limited by the allowable heating. Therefore, itis desirable to have a range of resist formulations with different α fordifferent profile depths or resist layer thicknesses. For a maximumprofile depth of D_(max) may in different contexts have a value higherthan 1.5/Dmax, 2/Dmax, 3/Dmax, 4/Dmax, or 5/Dmax, corresponding to amaximum writing dose of 4.5, 7.4, 20, 55, or 148 times higher than thedose that expose the top portion of the profile. Obviously every writingsystem also has some practical, thermal or throughput-related limit tothe highest dose E_(max) which puts an upper limit α_(max) on theabsorption such as 1000, 300, 100, 30, or 10 times the dose used toexpose the top of the profile E_(min). The value of α_(max) can becalculated as ln(E_(max)/E_(min))/D_(max). If D_(max) is one micron thenα will have to be smaller than 6.9, 5.7, 4.6, 3.4, or 2.3 per micron. Ina different example, the Fresnel lens above where D_(max) is 5 microns,α may be need to be smaller than 1.38, 1.14, 0.92, 0.68, or 0.46 permicron.

The absorption should preferably be matched to the resist thickness andthe dynamic range of the writing system. One way of doing this is by theselection of existing resists, e.g., dyed or colored resists. Anotherway is by adapting the writing wavelength to specific profile heightsand resists. A third approach is to add a passive or bleachableabsorbing compound to the resist formulation.

The scales are different in FIGS. 2 b, 3 a, and 4 a, in order tohighlight the basic function of each resist and process. A real resistand resist process will have both absorption and bleaching. The depth ofdevelopment will be affected by the finite dissolution rate. Thedissolution rate alone gives a depth increasing faster than proportionalto the exposure dose. A so-called bleaching resist will have a linearrelation between depth and dose. A so-called absorbing resist will havea depth function that grows slower than proportional with the dose. Themore that the absorption dominates, the more the depth vs. dose willresemble a logarithmic curve. Piecewise, we may express the depth asproportional to the dose raised to a constant k.

D(E)=k ₁ E ^(k)

where k₁ is a proportionality constant. One way to classify the resistprocesses is to name them according to the value of k:

Dissolution-like: k>1.5

Bleaching-like: 0.5<k<1.5

Absorption-like. k<0.5

Fresnel Lens Example

An example is that of the making of a Fresnel lens. The profile depth is5 microns and the required wavefront error is lambda/4 peak-to-valley at400 nm, i.e. +/−50 nm or +/−1% of the profile depth. Assume we need towrite the Fresnel lens pattern with a profile depth of 5 microns. Thedepth inaccuracy needs to be +/−50 nm or +/−1% of the full depth. If thelimit on dose E_(max) is 100 times E_(min) α can be up to 0.92 permicron. We can directly use the diagram in FIG. 4 a for Emax/Emin=100and find that the dose sensitivity is 0.22% of the full depth per %relative dose change. The allowed dose variation is then 1/0.22=5%, Thisis well better than the writing and development system's 3% control andwe can actually select a resist that has a lower α, e.g. α=0.64 permicron or we can use α=0.92 per micron and produce surfaces with threetimes better depth control, e.g. <+/−0.15% or 0.08λ peak-valley.

If we stay with α=0.92 per micron then we need 100 times higher dosethan the dose at the threshold as shown in FIG. 4. The relative doseaccuracy at the least dose need to be 5% i.e. the background noise inthe image has to be less than 1/100*5%=0.0005 of the highest dose.Therefore we need a writing system with a signal to noise of 2000:1.(The noise may come from internal reflections, non-perfect extinction inthe modulator, stray light, and inaccurate dose. Above all the writingsystem needs to have high contrast so the presence of the maximum dosein an area does not contaminate the clean exposure of the lowest one.The grey-value bitmap representing the dose needs to have at least asmuch dynamic range as the writing system, and in the examples above a12-bit representation may be suitable, corresponding to a signal tonoise of 4096:1, or in a different preferred embodiment of the presentdisclosure at least 10 bits or 1024:1. Previously known optical writershave 8-bit representations of the bitmap in optical writers and a signalto noise typically below 256:1.

The example discussed above shows that the useable α depends of theprofile depth and in order to write a variety of different profile depthit is useful to have a selection of resists with different α. Allresists have some level of absorption, and resists with added dyes tomake them more absorbing are known in the art, e.g. as a means to avoidreflecting notching on metal layers with topology. According topreferred embodiments of the present disclosure, the absorption in theresist used for producing three-dimensional patterns on a workpiece canbe made higher by addition of a dye or pigment, e.g. soot. Red, green,blue, and black resists made for LCD color filters can be used as aselection of resists with different absorption coefficients at thewriting wavelength.

Use of Multiple Focal Depths and Numerical Apertures

Another way to enhance the precision of latent image formation is toexpose the resist in N different passes with more than one focussettings in τhe z-direction. Different focal plane positions from thetop of the resist through the resist layer can be applied to differentexposure passes. By defining M different focus settings, the negativeeffects of the Gaussian-beam divergence can be reduced. Each of therelief depths within one layer will then be exposed with approximatelythe same Effective Spot Size. This is useful to improve the resolutionboth in the lateral x-y-direction and in the vertical z-direction.

FIG. 14 illustrates M=3 different focal planes. The N=3 separate,superimposed exposures are exposed with M=3 different focus settings. Apositive photoresist is assumed.

Pixel Sizes can Vary

FIG. 15 adds to FIG. 14 a representation of varying pixel sizes indifferent exposure phases. Each of the focal planes 1511, 1512, 1513 hasbeen given an individual grid size. A finer grid size 1513 is appliedwhere the relief features 1533 are sharpest. A fictive relief, with asharper tip deeper in the photoresist, is shown as a hatched line 1533.A positive photoresist is assumed. The of exposing 1521, 1532, 1534.There are a multitude of different possible methods to set the differentfocal planes, and to match those to the desired exposure doses at allthe certain depths, for all the N exposures, in the resist. Examples ofpossible exposure patterns embodiments are given below.

Selecting a Single Focal Plane

One approach is to use a simple linear interpolation between the Nlayers. Following this approach, layers which in turn may containseveral exposure doses which will reach different depths in the resistafter development (assuming a positive photoresist), may be assumed tobe exposed with an “average focus”.

One approach is to solve for an unknown focus vector:

$\min {\int{\int\limits_{x,y}{\left( {{E\left( {x,y,F,N} \right)} - {I\left( {x,y} \right)}} \right)^{2}\ {x}\ {y}}}}$

where E is the 2.5D surface after exposure, I is the ideal 2.5D surfacethat is the pattern, F is an vector with different focuses and N is avector with fixed different parameters that affect the exposure, forexample resist parameters, development time etc.

There are several ways to solve this equation above using commercialsoftware. One method is the Newton-Raphsons method; more generally,methods of non-linear optimization can be applied. Recall from abovethat the function E can be calculated as function of F. As a relativelycrude approximation, the E can be calculated using a convolution betweenthe object and some function that described the optical system(including or not including the development process). This method ofcalculating E is relatively fast and can be used for large patterns.Better, if the pattern repeats or if resources permit, one or more unitcell could be rigorously simulated using either commercial available orspecially developed software that simulates the exposure. For instance,a full propagation model and a complex chemical model for thedevelopment and process and circular boundary conditions could beapplied.

When solving the equation above, one can effectively start with onefocus layer, derive a result, then repeat the process adding more focalplanes one at a time until the merit function does not improve more thana certain limit. The maximum amount of focal planes can be set beforethe analysis begins or could be selected based on results of theanalysis.

Another approach is to approximate the exposure process of each of the Nexposures with a mathematical convolution of the exposing doses Forinstance, once can apply a Gaussian “kernel” and an “average focus”within each of the N exposures, for each of the depths that will bereached in the resist after the development. Perform the calculations ofthe N different 2-D convolutions, with the applicable Gaussian width andpeak value. Alter the outcome after comparison to the original relief,and once again perform the N 2-D convolutions. Iterate until the processconverges.

Another approximation of the multi-focal exposures can be obtained byapplying 3-dimensional convolution to calculate the exposure doses ofeach of the N individual exposures. That can be made by eitherapproximating the 3-dimensional convolution in the z-direction bydiscrete summations of the contributions from the N discrete exposures,or performing a 3-dimensional convolution using Volume pixel elements,or Voxels, throughout the entire volume of the photo-sensitive material.

Multiple Focal Planes

When using high resolution optics in combination with a thick resist youwill face the problem that the spot radius will vary through the resist.This will affect the resolution and you will get different resolution atdifferent Z-positions in the resist.

To improve fidelity over the full depth of the profile, use can be madeof a flexible, or adaptive, definition of (the N dose-boosting layers,and) the M focus layers by a first analysis of where the strongestgradients ∂z/∂x and ∂z/∂y are located in both the x- and y-directions,and—more important—in the z-direction. That may be done in a preparationsoftware processing system. For relief “pattern” details that have sharpz-direction details that produce high spatial frequencies at deep levelsin the photo-sensitive material, the corresponding focal planes wherethose relief details appear should be positioned deep in the material,preferably as deep as possible. For relief “pattern” details which havesharp z-direction details that produce high spatial frequencies atshallow levels in the photo-sensitive material, the corresponding focalplanes for those relief details should be positioned shallow in thematerial, or even at the resist surface. For relief “pattern” detailsthat have sharp z-direction details at intermediate levels in thephoto-sensitive material, the corresponding focal planes for thoserelief details should be positioned at intermediate depths. In allcases, the depth positioning of relief levels within the different focalplanes is arranged by the exposure dose. In practice, this means thatthe dose used to define the pattern is assigned to one of the focalplanes. Think of a pyramid with a sharp tip and a sharp angle where thesides meet the ground or floor. The area around the tip is exposed in awriting pass with focus near the tip, and the lower parts of the sidesare exposed in a pass with focus near the ground. Each pass is describedby a bitmap, and the low-focus bitmap contains only zeros around thetip, so that the bitmap in the high-focus bitmap determine the shape ofthe tip. For xy coordinates corresponding to the lower parts of thesides, the high-focus contains zeros or small values and the surfaceshape is determined by the data in the low-focus bitmap. In intermediateareas both bitmaps have non-zero data and the exposure dose is dividedbetween the two passes.

If the pyramid is low compared to the focal depth, one pass with asingle focus setting may be enough. If, on the other hand, the pyramidis high compared to the depth of focus two passes may not be enough todefine details on all levels, and more passes and focus levels may beused. The dose at a specific xy point is then assigned to one or morepasses which give the best 3D fidelity to the data. To determine thenumber of passes needed and how to assign the doses to the layers, i.e.to determine the layer bitmaps, in the presence of complex patterns,absorption, bleaching, defocus and developer kinetics is a non-trivialtask. We disclose for this purpose software algorithms and hardware todo this automatically.

In other circumstances, the dose setting of the N exposures can beincorporated into the non-linear exposure characteristics of thephoto-sensitive material, which in a 3-D application is shown by itsdepth-vs-dose function. One of the root causes to the non-linearity ofthe photoresist depth-vs-dose response is the so-called bleaching thatresults from depletion of the photo-active compound (PAC) during theabsorption of the exposing radiation/electromagneticradiation/light/laser light. Compensating for non-linear effects andbleaching effects is useful when setting doses in an N-exposure writingscheme.

Impact of Thickness on Divergence

FIGS. 16 and 17A depict beam divergence patterns in resist layers thatare 1 and 80 μm thick, respectively. FIG. 17B is an enlargement of asection of the 80 μm thick resist, which shows a section 5 μm thick andmakes it easier to visualized convergence and divergence pattern in thethick resist. In FIGS. 16-17, the vertical axis is scaled to match theresist thickness. Accordingly, the axes have much different scalingfactors. In each figure, the focal plan is set to the middle of theresist layer. For the 1 μm thick resist in FIG. 16, exposure is in atight column, with relatively little divergence. For the 80 μm thickresist, FIG. 17B is provided to improve comprehension of the convergenceand divergence pattern in the 80 μm thick resist. From this enlargedsimulation result, one can see a so-called waist in the focus thatextends about +/−300-400 nm on either side of the “0” position focalplane. Within about +/−1.5 μm of the focal plane for the 80 μm thickresist, the beam is workably narrow. The reported numerical aperture of0.55. In air, this would correspond to a half-angle of about 33 degreesor a focal cone of about 67 degrees. The resist is specified as havingan X² response. The refractive index is not given in the figures, butmay have been about 1.5, which is less than 1.7, which is a reasonabletarget value. Divergence produces rounding of some features in a latentimage.

A usefully precise measure of beam divergence and, therefore, of depthof focus is the so-called Rayleigh range. Applying the Rayleigh rangez_(R) as the criteria for the depth of focus, the Rayleigh range extendsa distance on either side of the focal plane for which the beamcross-section is not larger than square root of two times the diameterof the beam cross-section at the best focal plane. We use two times theRayleigh range distance as the depth of focus, as further explainedbelow.

The depth of focus can be defined in many ways. In practice, the usabledepth of focus is often determined empirically as the largest focuslatitude that is compatible with acceptable yield. This practicalapproach depends on the design, performance specifications and economicvalue of the structures produced.

For patent purposes and in this disclosure, we use the followingdefinition of the depth of focus DOF, as twice the Rayleigh range z_(R)for a beam which is Gaussian or approximately Gaussian. Mathematically,

DOF=2z _(R)=2πw ₀ ²/λ=2λ/(πNA²)

where w₀ is the 1/e² beam radius at the beam waist. It is related to NAthrough

w ₀=2λ/(∂Θ)=λ/(πNA)

where NA is Sin(Θ/2) and Θ/2 is the angle from the center line of adiverging beam where the intensity has fallen to 1/e² of the value atthe center. λ is the wavelength in the medium, in this case, thewavelength in the resist, which typically has a refractive index ofabout 1.7 for UV wavelengths. The formula uses the paraxialapproximation where sin(Θ/2)=Θ/2. For some optical systems, inparticular image-projection systems using partially coherentillumination, the definition DOF=λ/NA² applies to fairly approximate thedepth of focus. The difference between DOF=21λ/(λ/NA²) for a Gaussianbeam and λ/NA² for an imaging system comes partly from the differentphysics, partly from the top hat vs. Gaussian filling of the NA withlight.

For some purposes, it is useful to define thin and thick resist usingthis Rayleigh range definition of depth of focus. We define thin resistto have a vertical thickness of less than or equal to one or two timesthe depth of focus. Thick resist has a vertical thickness of greaterthan or equal to either four or five times the depth of focus. In thinresist, convergence and divergence effects are relatively moderate. Inthick resist, convergence and divergence effects should, in the view ofthese inventors, be taken into account explicitly. Either four or fivetimes the depth of focus can be chosen as a practical definition of whena resist is considered thick for purposes of this disclosure. We willuse these definitions of thin and thick resist throughout thisdisclosure.

Impact of Focal Plane Choice on Pattern

FIG. 18 shows the difference between ideal and exposed in a 20 μm resistlayer, when the focal plane is set at 10 μm. The ideal feature hasvertical sides, like a semi-sphere. The resulting exposure has aninflection point at about the focal plane, witching from a convex solidto a converse solid. The differences graph of FIG. 18 dramaticallyillustrates the formation of fillets where the feature sides aresupposed to be vertical.

The conventional patterns for lithography in 2D do not translate well to2.5D because 2D patterns are usually binary: the resist is eitherexposed or not. Greyscale values are only used for the positioning ofthe edge with subpixel accuracy. In 2.5D applications, each greyscalevalue is mapped to a specific thickness after development of the photoresist. Thus, the pattern for a 2.5D feature will contain much more greyscale values than patterns used for 2D lithography.

Gradients to Select Focal Plane(s)

For thick resist, one or more focal planes are selected to bestreproduce the ideal feature in the thick resist layer. To select asingle focal lane for the semi-sphere, for instance, a computer can beused to calculate gradients across the x and y grid, either from apixelmap or for a pattern described by mathematical functions. Thecomputer then calculates the normal vector either directly from thegradients or from a filtered version, either from a linear filteredversion or a non-linear filtered version, of the gradients. Then foreach z-height (the total thickness will be divided into severalsubsections), a distribution of the angles between the normal vector andXY-plane will be calculated.

By analyzing the distribution of the normal vector directions for thesez-heights, the computer can select or assist a user in selecting focalplanes at various z-heights that give a close match between the idealfeatures and the exposed result. An optimization search for a focalplane height can use linear or non-linear techniques. The penaltyfunction used can be a function of the focus-height, z-height, thenormal vector angle, or another measure.

FIG. 19 applies this algorithm to the semi-sphere pattern, depictinggradients and the gradient distribution. The data in the lower graph ofFIG. 19 together with a distribution function for gradients at eachz-height can be used to select the correct focal plane. A simpleselection approach selects one focal plane. In the example above, theselection ignore average gradients below the so-called relaxation limitof 200. Depending on the geometry and desired sharpness of verticalcorners, the relaxation limit may be higher or lower. In the top graphof FIG. 19, there is one pair so-called vertical corners, both at thesame z-height, where the flat horizontal runs abruptly turn upward atthe vertical edges of the semi-spheres. In the lower graph of FIG. 19,which plots the absolute value of average gradients against verticalposition within the relief map or resist layer, the position of allvertical corners at the same height produces one peak in the graph. Thefocal plane is selected as depicted in FIG. 20. The relaxation limit,indicated by the horizontal dotted line, is used to isolate the part ofthe pattern in which the focal plane will be located. The position ofthe focal plane is selected based on a centre of gravity of the areaabove the relaxation limit. In FIG. 20, the area is a triangle andcalculated focal plane height is around 0.27 μm.

The selection of a number of focal planes used to cover a single areaabove the relaxation limit will depend on the vertical extent beingexposed, as a ratio of the depth of focus. The greater the availabledepth of focus, the greater the vertical extent of resist that can beeffectively exposed by a focus in a single focal plane. In FIG. 20, thevertical extent of resist near the vertical corner and having a highaverage gradient is indicated by the base of the triangle. When thisbase is longer than some threshold factor of the depth of focus,multiple exposures will be needed. The factor may be one or two, whichcorresponds to our definition of a thin resist. When the depth ofexposure exceeds the threshold, the vertical extent is partitioned intotwo or more vertical extents and focal planes are selected for themultiple vertical extents. Alternatively, if the number of focal planesallowed for exposing the resist layer is lower than the number ofsubsections, the focal planes are distributed in order to minimize thesum of the least squares norm (sometimes called the L2 norm) betweeneach center of gravity and the closest focal planes.

FIG. 22 depicts a more complicated 2.5D relief, with a pillar and cap ontop of an ellipse. Vertical corners are at about 0, 8 and 12 micronsheight. These corners are apparent in both the cross section in the topof FIG. 22 and the average gradient peaks in the bottom of the figure.Note the peak 2 and 3 is lower than the first one since the averageabsolute value of the gradient is calculated within a height intervaland the sharp step only contains one sample point. The relaxation limithas adaptively been set at 50, to capture all three peaks. Preferably,three focal planes are selected. With three focal planes available, thealgorithm will here place the planes at 0.27 μm, 8.25 μm and 12.25 μm.If a fewer focus layers are allowed, the algorithm may focus on thegradient peaks in the bottom graph of FIG. 22 that have highest Z-heightcomponents. For example if two focus layers were allowed it would havebeen 0.27 μm and 8.25 μm in the case above. Alternatively, if less thanthree are available, the sum of least squares between centers of gravityand focal planes can be calculated to position the focal planes. Or,where there are dominant peaks, as in FIG. 22, focal planes can beallocated to those peaks and the one of the least squares approachesdescribed above can be applied to position the remaining peaks. This, ofcourse, depends on having enough focal planes available to cover thedominant peaks and the remaining vertical segments that are outside thedepth of focus of the focal planes selected to cover the dominant peaks.

Several variants of the algorithm are readily available. On could, forexample, change the selection function to use maximum gradients inareas, instead of average gradients. Or, one could use a function thatis based on higher moments than the gradient. The selection function canalso vary. For example, based on calculating a mean instead of centre ofgravity or matching focal planes to the gradient peaks.

With multiple focal planes, one should understand that doses aredistributed among the focal planes, with doses emphasized in anyplane(s) that contain a vertical corner. In FIG. 21, an x, y coordinatewill have only one vertical corner at one height in one focal plane. InFIG. 22, some x, y coordinates have two vertical corners at differentheights, so the dose will be distributed between the focal planesclosest to the top and bottom of the pillar on top of the ellipse.

FIGS. 22-23 are photo micrographs of some features in resist that wereformed using differently positioned focal planes. FIG. 22 had its focalplane selected by applying the approach described. FIG. 23, in contrast,was exposed with a less well chosen focus setting. FIG. 22 has sharperedges, as a result of the focal plane selection.

The method above can also be generalized by further allowing for severalfocus layers. These focus layers can be written in one pass bydynamically changing focus or using a writing engine that can write toseveral focal depths simultaneously, e.g. a multibeam writer withdifferent focus for each beam or a SLM/DMD writer with a tilted focalplane over the chip. Alternatively, the data can be divided into severalpasses that are written separately with different focus settings.

If several focus settings are allowed, the basic optimization is thesame as above except for that the optimization restraints are changed toallow multiple focus layers. The algorithm will then label each pixel toa certain focus layer.

Pattern Decomposition

FIG. 24 illustrates how the algorithm may divide the pattern into twolayers with different focus.

FIG. 25 illustrates the result assuming that the pattern is alreadydefined. FIG. 26 shows a flow chart for the algorithm.

Some Particular Embodiments

The present invention may be practiced as a method or device adapted topractice the method. The invention may be an article of manufacture suchas media impressed with logic to carry out computer-assisted formulationof an exposure map for three-dimensional patterning of resist.

Some Methods

The first method embodiment forms a three-dimensional latent image withgood depth and shape control in a resist layer 2673 applied over aworkpiece 2683. This method is particularly well adapted to a thinresist layer 2673, such as resist layer that is thinner 2663 than thedepth of focus of exposing system used the pattern to resist, which isdefined above as twice a Rayleigh range 2676. It also may be applied toa moderately thin resist layer that is no more than twice as thick asthe depth of focus of the exposing tool.

This method includes using a positive resist with an effectiveabsorption characteristic that produces a log-linear relationship 2651between the exposing energy and the depth of exposure. This log-linearrelationship may otherwise be described as an exponential relationship,which is the inverse a log-linear relationship. The equations for afirst-order approximation of the log-linear or exponential are given inthe disclosure above. By first-order approximation, we mean that a moreprecise curve fit to calibration data can be achieved by addingadditional terms or by taking into account processes in addition to thedominant absorbing process.

The method proceeds with converting a relief map that represents athree-dimensional surface 2611 into point-by-point exposure doses 2691calculated to reach an exposure threshold of the positive resist at aplurality of controlled depths within the resist layer 2673. When theexposure doses are calculated, the calculation takes into account thelog-linear relationship. An exposure map is produced. This exposure mapmay be prepared ahead of patterning and persisted for later use, or itmay be as needed for patterning and consumed by a pattern generatorclose to the time that is prepared. Preparing the exposure map inadvance may have the advantage of facilitating simulation andimprovement.

This method optionally includes patterning the resist layer to form athree-dimensional latent image using a pattern generator 2615-2635 thatvaries effective exposure doses 2691 on a point-by-point basis using theexposure map.

This method can be extended by developing the latent image and producinga device using the developed latent image. The device may be produceddirectly or by replication. Examples of devices produced from 3-Dpatterning of resist are given in the disclosure above. One immediateexample is a lenticular lens for three-dimensional viewing of an image.Alternatively, it may represent the relief map to a precision of atleast 11 binary bits and use the 11-bit precision to produce exposuredoses. Or, it may be calibrated to produce at least 1000 or 4000 dosesteps between minimum and maximum exposure doses.

The positive resist used in the foregoing method may be a bleachableresist. By bleachable 2677, we mean including a component that absorbsphotons, is converted by the photons, and is substantially a lessabsorptive after the conversion. This bleachable component may beessentially opaque prior to bleaching and transparent or translucentafter bleaching. This component may make the resist layer opaque, beforebleaching.

The effective absorbed a characteristic of the positive resist mayresult from passive absorption 2678. That is, the positive resist mayinclude an effective quantity of a passive absorbing component thatabsorbs photons without chemically exposing the resist, for instance,converting the photons to heat. An effective amount of passive andabsorbing components may be used to cause a log-linear relationship 2651between exposure energy and depth of the exposure. Two examples ofpassive absorbing components are dye and nano-particles, such as soot.

When a log-linear relationship 2651 is present, the lower half of theresist (below 2675), further away from the surface that is exposed thanthe upper half of the resist (above 2675), requires more marginal energyto expose then the upper half. If the upper half uses one unit ofenergy, the lower half may use 2, 3, 4, 5 or more times as much energyas the upper half Any of these proportions such as at least 3, may hold.When the lower half requires twice the “one unit” of exposing energy asthe upper half, the total energy required to expose both halves will bethree units. Of course, reference to units in this context is referenceto arbitrary units. Alternatively, the lower quarter of the resistrequires 100 times as much marginal exposure energy as the upperquarter.

The positive resist used in this method may have a gamma of five orgreater (FIG. 2 a). Alternatively, the resist may have a gamma of 8 orgreater.

The pattern generator used may be a laser pattern generator 2615-2635.

A second method embodiment forms a three-dimensional latent image withgood depth and shape control in a thick resist layer applied over aworkpiece 2683. A thick resist layer may be 1.5 times as thick 2763 asthe depth of focus of the pattern generator used to expose the resist,where the depth of focus is twice a Rayleigh range 2776. Alternatively,a thick resist layer may be twice as thick 2763 as the depth of focus.As illustrated in the figures, a thick resist alternatively may be atleast three times as deep as the depth of focus.

This method proceeds using a thick positive resist that has a gamma offive or greater (FIG. 2 a). Alternatively, the resist may have a gammaof 8 or greater. A gamma value corresponds to the steepness of exposureto dissolution rate curve, as illustrated in the figures. The higher thegamma, the narrower the dose band that moves the resist from having avery low dissolution rate to having a very high dissolution rate. A highgamma resist is also said to be a high contrast resist. It is suitablefor endpoint or essentially endpoint processing. By essentiallyendpoint, we mean that the resist is dissolved until the rate ofdissolution has dropped off very substantially, so that the developmentand dissolution process is relatively insensitive to the developmenttime allowed. In contrast, the low gamma resist is often uses acarefully timed the etching process, giving a relief depth that isproportional to the etching time. A timed process, of course, issensitive to etching time and other development-related factors.

The value of gamma is a function of the type of resist chemistry, theresist concentration of the PAC, the baking time and temperature, andthe developer. The dissolution is very slow up to a threshold value, andgrows approximately linearly for high doses. The high contrast isachieved at the knee between very low dissolution rate and a dissolutionrate which grows fast with the exposure dose. Therefore, the gamma valueis high when development is slow and fast development means moving up onthe linear part of the dissolution curve, giving low contrast and gamma.The gamma is therefore as much a property of the process, as of theresist material, and it is known that cold diluted developer producesvery high gamma in some resist formulations. On the other hand,published dissolution curves in descriptions of laser- and ebeamprocesses for 3D (or 2.5D) surfaces often shows an approximately linearrelation between remaining thickness and dissolution rate, i.e. a gammaaround 1.

This second method proceeds with converting a relief map that representsa three-dimensional surface 2611 into point-by-point exposure dosescalculated to exceed an exposure threshold of the positive resist at aplurality of controlled depths within the resist layer. The calculationoptionally takes into account the numerical aperture 2656 of theexposing system. The numerical aperture value can be taken into accountanalytically or by empirical observation of in exposure of resist usingdifferent numerical apertures. The converted relief map results inexposure map will, as described above.

This method optionally proceeds with patterning the resist layer inmultiple writing passes to form a three-dimensional latent image. Thepatterning uses a high dynamic range pattern generator 2615-2635 thatvaries exposure doses on a point-by-point basis using the exposure map2691. By high dynamic range, mean a pattern generator calibrated produceat least 1000 steps between minimum and maximum exposure doses. It mayuse 11 binary bits or more precision. Alternatively, the patterngenerator may be calibrated to produce at least 4,000 steps betweenminimum and maximum exposure doses.

The positive resist used in the foregoing method may be a bleachableresist. By bleachable 2677, we mean including a component that absorbsphotons, is converted by the photons, and is substantially a lessabsorptive after the conversion. This bleachable component may beessentially opaque prior to bleaching and transparent or translucentafter bleaching. This component may make the resist layer opaque, beforebleaching.

The resist may have a passive absorption characteristic. That is, thepositive resist may include an effective quantity of a passive absorbingcomponent that absorbs photons 2678 without chemically exposing theresist, for instance, converting the photons to heat. An effectiveamount of passive and absorbing components may be used to cause alog-linear relationship between exposure energy and depth of theexposure 2651. Two examples of passive absorbing components are dye andnano-particles, such as soot.

The pattern generator 2615-2635 used may be a laser pattern generator.

Aspects of the first and second methods can be interchanged orrecombined, as typically expressed in a dependent claim that dependsfrom any of the forgoing claims. They also may be combined with featuresdescribed in the foregoing disclosure.

A third method forms a three-dimensional latent image with good depthand shape control in a thick resist layer 2863 applied over a workpiece2883. The meaning of thick resist in this method is as above. Of course,aspects of the first and second methods can be interchanged andrecombined with aspects of the third method, as above.

The third method proceeds using a positive resist. It includes selectingmultiple focal planes 1511, 1512, 1513 at which to focus exposingenergy. At least one of focal planes 1513 is in a lower half of theresist layer. By lower half, we mean the half of the resist that isfurther from a surface to which exposing energy 2855 is applied than theupper half.

This method continues with converting a relief map that represents athree-dimensional surface into point-by-point and layer-by-layer andexposure doses 2691 calculated to exceed an exposure threshold of thepositive resist at a plurality of controlled depths within the resistlayer. The calculation takes into account the numerical aperture value2656 to be used during patterning. Different numerical apertures may beapplied to different focal planes. Applicable numerical apertures may beautomatically selected. The method produces an exposure map 2691.

This method optionally proceeds with patterning the resist layer usingthe multiple focal planes to form a three-dimensional latent image,using a pattern generator 2615-2635 that varies effective exposure doseson a point-by-point basis using the exposure map 2691.

Another optional aspect of this method is selection of the focal plane1513 in the lower half of the resist layer (below 2675) to emphasizeaccurate patterning of vertical or near-vertical aspects of features(e.g., 501, 1911) in the relief map. By vertical, we mean perpendicularto the surface of the workpiece 2883. Multiple focal planes can beautomatically selected by identifying two or more vertical corners 2111,2113, 2115 in features in the relief map that are at different verticalheights within the relief map and selecting two or more focal planes1511, 1513, 1515 corresponding to the two or more corners andpositioning them to enhance the three dimensional latent image of thevertical corners.

Alternatively, the focal plane in the lower half of the resist may beselected to emphasize accurate patterning of features in the relief mapthat have sharp z-direction details 1533. Or, the focal plane in thelower half may be selected to emphasize accurate patterning of featuresin the relief map that have relatively high spatial frequencies, ascompared to other features in the relief map.

As in the second method, the pattern generator 2615-1635 used in thethird matter used in the third method may have a high dynamic range.That is, it may be calibrated to produce at least 1000 dose stepsbetween minimum and maximum exposure doses, to use at least 11 bitsprecision, or to produce at least 4000 dose steps.

Optionally, pixels of different sizes (FIG. 15) can be used in themultiple focal planes 1511, 1513, 1515.

Exposure in the different focal plans may be accomplished in a singlewriting pass by a pattern generator that supplies multiple beams 2855that are focused in the different focal planes (FIG. 28). The patterngenerator may expose the multiple focal planes in multiple writingpasses 2832.

Exposure doses are allocated among layers 1511, 1513, 1515 and stored inthe exposure map 2691 on a layer-by-layer basis. There are a variety ofalternative ways of allocating exposure doses among the focal planes.

As described above, the allocation of doses among layers may involveapplying linear interpolation, or 2D convolutions applied at depthsselected from the relief map, or 3D convolutions simulating writingexposures in the multiple focal planes. The simulation may involve fully3D convolutions, using volume pixel elements, also known as voxels.

This method may automatically select and/or position focal planes 1511,1513, 1515. It may select one focal plane or two or more focal planes.It may automatically position any number of focal planes, whetherselected automatically or by an operator.

The pattern generator 2615-2635 may be a laser pattern generator.

A fourth method forms of a three-dimensional latent image with gooddepth and shape control in a layer of resist 2673, 2773 applied over aworkpiece 2683, 2783. It involves two or more iterations 2903 to improvean exposure map 2901. The method proceeds with converting a relief mapthat represents a three-dimensional surface 2611 into point-by-pointexposure doses 2901. The point-by-point exposure doses are calculated toexceed an exposure threshold of the resist at a plurality of controlleddepths within the resist layer, producing an exposure map.

The method proceeds with two or more iterations 2903 of simulating on acomputer 2902 the patterning of the resist layer with a patterngenerator that varies effective exposure doses on a point-by-point basisusing the exposure map. This simulating produces a simulatedthree-dimensional latent image 2925, 2926. The simulatedthree-dimensional latent image 2925, 2926 is compared 2924 to the reliefmap 2611. The exposure map is revised using results of the comparing.

This method may iterate 2903 five or ten times or more.

A further aspect of this method involves calculating a sweep adjustmentduring the converting of the relief map. A sweep adjustment takes intoaccount a direction of travel of exposing radiation across the resistlayer and compensates for non-linear effects related to whether theexposure is building or diminishing (FIG. 5) as the exposing radiationmoves across the resist layer. The calculated sweep adjustment may beincorporated into the exposure map.

This method also may include the simulating step taking into account thedirection of travel of exposing radiation (FIG. 5) across the resistlayer and non-linear effects related to whether exposure is building ordiminishing as the exposing radiation moves across resist layer.

The resist used in the foregoing method may be a positive, bleachable2677 resist. By bleachable, we mean including a component that absorbsphotons, is converted by the photons, and is substantially a lessabsorptive after the conversion. This bleachable component may beessentially opaque prior to bleaching and transparent or translucentafter bleaching. This component may make the resist layer opaque, beforebleaching.

The resist may have a passive absorption characteristic. That is, thepositive resist may include an effective quantity of a passive absorbingcomponent 2678 that absorbs photons without chemically exposing theresist, for instance, converting the photons to heat. An effectiveamount of passive and absorbing components may be used to cause alog-linear relationship 2651 between exposure energy and depth of theexposure. Two examples of passive absorbing components are dye andnano-particles, such as soot.

This iterative method may be applied to refine any of the foregoingmethods of forming a three-dimensional latent image. In a thick layer ofresist, this method may be extended by defining multiple focal planes1511, 1513, 1515 at which to focus exposing energy. The relief map maybe converted into point-by-point and layer-by-layer exposure doses,producing the exposure map 2691, 2901. The simulation, in turn, proceedstaking into account the multiple focal planes.

The meaning of a thick layer in this extension of the fourth method isas described above. The positive resist the simulated may have a gammaof five or greater or, alternatively, eight or greater. This simulatingmay take into account the numerical aperture 2656 of the patterngenerator 2615-2635 when writing to the multiple focal planes. Thesimulated pattern generator and may be a high dynamic range patterngenerator that is calibrated to produce a least 1000 dose steps betweenminimum and maximum exposure doses, or that is calibrated to produce atleast 4000 dose steps.

The iteration may be continued beyond one refinement, repeating thesimulating, comparing and revising actions until results of comparingthe difference 2924 between successive simulated three-dimensionallatent images 2925, 2926 satisfies a predetermined criterion.

In a thick resist layer, the method may further include definingmultiple focal planes 1511, 1513, 1515 at which to focus exposing energy2655, 2855, converting the relief map into point-by-point andlayer-by-layer exposure doses 2691, the exposure doses allocated bylayer, producing the exposure map 2901, and simulating the patterning ofthe resist layer 2925, 2926 using the multiple focal planes.

Focal plane positions and/or counts may be automatically selected basedon data in the relief map, such as data that describes vertical corners.

A thick layer may be as described above, 1.5 or two or three or moretimes the depth of focus of a pattern generator.

The resist may have a gamma of 5 or 8 or greater.

The simulating may take into account a numerical aperture 2656 of thepattern generator 2615-2635, which may change from one focal plane tothe next or one writing pass to the next.

The simulated pattern generator may be configured to produce at least1000 dose steps, or to use at least 11 binary bits precision or toproduce at least 4000 dose steps.

This method optionally includes using a pattern generator, such as alaser pattern generator, to apply the refined exposure map to patterninga thin or thick layer of resist applied to the surface of a workpiece.As previously mentioned, the method may be extended by developing theresist and producing devices using the developed resist.

The pattern generator may be a laser pattern generator.

Devices that Practice the Methods

Each of the methods described above involve close cooperation amongspecialized hardware components. Maps are stored in memory. Mapprocessors are used to convert maps and apply transfer functions.Simulation processors are used to conduct simulations. Lasers, lensesand resist are used to form latent images on workpieces. The lasers andresists have a variety of alternative characteristics, as describedabove. Depending on the application, the map and simulation processorsmay determine point-by-point exposures for different thicknesses andcharacters of resist.

Articles of Manufacture

While the present invention is disclosed by reference to the preferredembodiments and examples detailed above, it is understood that theseexamples are intended in an illustrative rather than in a limitingsense. Computer-assisted processing is implicated in the describedembodiments. Accordingly, the technology disclosed may be embodied inmethods for calculating exposure doses and writing passes to create 2.5Dlatent images in resist with a high gamma. It may be embodied in systemsincluding logic and hardware resources to calculate exposure doses andwriting passes, systems that take advantage of computer-assistedcalculation of exposure doses and writing passes, computer readablestorage media impressed with logic to carry out calculation of exposuredoses and writing passes, data streams impressed with logic to carry outcalculation of exposure doses and writing passes, or computer-accessibleservices that carry out computer-assisted calculation of explore dosesand writing passes. It is contemplated that modifications andcombinations will readily occur to those skilled in the art, whichmodifications and combinations will be within the spirit of theinvention and the scope of the following claims.

The methods, devices and articles of manufacture can be combined with orapplied using a writing system as described, thereby creating a 2.5Dlatent image in the resist layer. The 2.5D latent image can be developedto produce a 2.5D structure. The 2.5D structure might be used directlyor may be used as masters for replication and production ofmicro-structures, as generally described above. The resulting structuresmay be optical, mechanical, fluidic or similar component or devices.

1. A method of forming a three-dimensional latent image with good depthand shape control in a layer of resist applied over a workpiece surface,the method including: converting a relief map that represents athree-dimensional surface into point-by-point exposure doses calculatedto exceed an exposure threshold of the resist at a plurality ofcontrolled depths within the resist layer, producing an exposure map;and repeating for two or more iterations, simulating the patterning ofthe resist layer with a pattern generator that varies effective exposuredoses on a point-by-point basis using the exposure map to produce asimulated three-dimensional latent image, comparing the simulatedthree-dimensional latent image to the relief map, and automaticallyrevising the exposure map using results of the comparing.
 2. The methodof claim 1, wherein the method further includes repeating for five ormore iterations.
 3. The method of claim 1, wherein the convertingfurther includes calculating a sweep adjustment that takes into accounta direction of travel of exposing radiation across the resist layer andcompensating for non-linear effects related to whether exposure isbuilding or diminishing as the exposing radiation moves across theresist layer, and incorporating the calculated sweep adjustment into theexposure map.
 4. The method of claim 2, wherein the simulating takesinto account a direction of travel of exposing radiation across theresist layer and non-linear effects related to whether exposure isbuilding or diminishing as the exposing radiation moves across theresist layer.
 5. The method of claim 1, wherein the resist is a positiveresist that includes a bleachable absorption component that is convertedby the exposing radiation and substantially loses it absorptivenessduring the patterning, whereby the bleachable components cause a linearrelationship between exposure energy (E) and the depth of exposure (D).6. The method of claim 1, wherein the resist is a positive resist thatincludes an effective quantity of passive absorption component thatabsorbs photons without chemically exposing the positive resist, wherebythe passive absorption component causes a log-linear relationshipbetween exposure energy (E) and the depth of exposure (D).
 7. The methodof claim 1, wherein the layer is a thick layer of resist, furtherincluding: defining multiple focal planes at which to focus exposingenergy; converting the relief map into point-by-point and layer-by-layerexposure doses, the exposure doses allocated by layer, producing theexposure map; and simulating the patterning of the resist layer usingthe multiple focal planes.
 8. The method of claim 7, further includingautomatically selecting a number of focal planes based on detection ofvertical corners in the relief map.
 9. The method of claim 8, furtherincluding automatically selecting positions of one or more focal planesbased on data in the relief map.
 10. The method of claim 8, furtherincluding automatically selecting positions of two or more focal planesbased on data in the relief map.
 11. The method of claim 8, wherein thethick resist layer has a vertical thickness that is greater than orequal to 1.5 times a depth of focus of the pattern generator during thepatterning, wherein the depth of focus is twice a Rayleigh range. 12.The method of claim 8, wherein the thick resist layer has a verticalthickness that is greater than or equal to two times a depth of focus ofthe pattern generator during the patterning, wherein the depth of focusis a twice Rayleigh range.
 13. The method of claim 1, wherein the resistis a positive resist that has a gamma of 5 or greater.
 14. The method ofclaim 7, wherein the simulating takes into account a numerical apertureof the pattern generator when writing to the multiple focal planes. 15.The method of claim 1, wherein the pattern generator is a high dynamicrange pattern generator that is calibrated to produce at least 1000 dosesteps between minimum and maximum exposure doses.
 16. The method ofclaim 1, wherein the pattern generator is a high dynamic range patterngenerator that is configured to write at least 4000 dose steps betweenminimum and maximum exposure dose.
 17. The method of claim 1, whereinthe pattern generator is a high dynamic range pattern generator thatrepresents the relief map to a precision of at least 11 binary bits anduses the 11-bit precision to produce exposure doses.
 18. The method ofclaim 1, further including patterning the resist layer to form athree-dimensional latent image using a pattern generator that varieseffective exposure doses on a point-by-point basis using the exposuremap.
 19. The method of claim 18, wherein the pattern generator is alaser pattern generator.
 20. The method of claim 1, further includingrepeating the simulating, comparing and revising actions until thecomparing results in a difference between successive simulatedthree-dimensional latent images that satisfies a pre-determinedcriterion
 21. The method of claim 1, wherein the converting furthertakes into account and compensates for non-linear effects related tofeature precision requirements, feature area and/or the gradient field.22. The method of claim 1, wherein the converting further takes intoaccount and compensates for etch rate or dissolution rate selected. 23.The method of claim 1, wherein the converting further takes into accountand compensates for the etch rate or dissolution rate selected.
 24. Themethod of claim 1, wherein the converting further uses pre-determinedrules and/or a model to compensate for non-linear effects.